# STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching

arXiv: https://arxiv.org/abs/2603.08478 · HTML: https://mlsanity.com/paper/2603.08478/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Dynamics-Guided Diffusion Model for Sensor-less Robot Manipulator Design](https://mlsanity.com/paper/2402.15038/) (2024)
- [Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid](https://mlsanity.com/paper/1410.7284/) (2014)
- [PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2409.09441/) (2024)
- [Agile Continuous Jumping in Discontinuous Terrains](https://mlsanity.com/paper/2409.10923/) (2024)
- [Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotion](https://mlsanity.com/paper/2506.16079/) (2025)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Floating-Base Deep Lagrangian Networks](https://mlsanity.com/paper/2510.17270/) (2025)
- [Real-Time Gait Adaptation for Quadrupeds using Model Predictive Control and Reinforcement Learning](https://mlsanity.com/paper/2510.20706/) (2025)

## Abstract (arXiv)

Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated impressive performance, many deployment settings still require predictive models that support planning, constraint handling, and online adaptation. Analytical rigid-body models provide strong physical structure but often fail to capture complex interaction effects, whereas purely data-driven models may violate physical consistency, exhibit data bias, and accumulate long-horizon drift. In this work, we propose STRIDE, a dynamics learning framework that explicitly separates conservative rigid-body mechanics from uncertain, effectively stochastic non-conservative interaction effects. The structured component is modeled using a Lagrangian Neural Network (LNN) to preserve energy-consistent inertial dynamics, while residual interaction forces are represented using Conditional Flow Matching (CFM) to capture multi-modal interaction phenomena. The two components are trained jointly end-to-end, enabling the model to retain physical structure while representing complex stochastic behavior. We evaluate STRIDE on systems of increasing complexity, including a pendulum, the Unitree Go1 quadruped, and the Unitree G1 humanoid. Results show 20% reduction in long-horizon prediction error and 30% reduction in contact force prediction error compared to deterministic residual baselines, supporting more reliable model-based control in uncertain robotic environments.